The neutron number probability distribution in coupled lumped assemblies

Abstract

The validity of the gamma distribution in describing the neutron number probability distribution function for both isolated and coupled multiplying assemblies when constrained to reproduce the true mean and variance is investigated in lumped geometry by numerical comparison with kinetic Monte Carlo simulations. The mean and variance are obtained from numerical solution of moment equations constructed from the relevant forward Master equation with assembly coupling coefficients obtained from a view factor method. Numerical results for a two-group, two coupled assemblies model, with static and dynamic reactivity insertion, show that except for subcritical assemblies, the gamma distribution well-approximates the number distribution. Differences in the fast and thermal neutron population shapes are explained in terms of effective source strengths due to downscatter and coupling.